Pulsed Noise - Based Stochastic Optimization with the Hopfield Model

In this paper a new, simple approach to solving combinatorial optimization problems is discussed and preliminary simulation results are presented. The Pulsed Noise Model (PNM) introduced in the paper is based on combining the Langevin Equation minimization method with the Hopfield model, in a very straightforward manner. The main advantage of this approach is its conceptual simplicity without sacrificing efficiency. Unlike in the previous related works (stochastic neural networks, diffusion machine), in the PNM, intensities of gaussian noises injected to the system are independent of neuron’s potentials. Moreover, in PNM noises are injected to the system only at certain time instances in the opposite to continuously maintained -correlated noises used in previous approaches. Finally, instead of impractically long inverse logarithmic cooling schedules, the linear cooling is applied. Definitely, with the above strong simplifications PNM is not expected to rigorously maintain Thermal Equilibrium (TE). However, approximate numerical test based on the canonical Gibb-Boltzman distribution show, that differences between the rigorous and estimated values are relatively low (withina few percent). In this sense PNM is said to perform Quasi-Termal Equilibrium.